Servomechanism with adjustable predictor filter

ABSTRACT

A digital control system, and in particular a tape drive system having a track-following servomechanism with a predictor (also referred to herein as a predictor filter), is described. In certain embodiments, the servomechanism includes an actuator, a servo channel, and a predictor coupled to the servo channel. The predictor receives from the servo channel a lateral position estimate signal and determines a modified lateral position estimate signal that reduces a difference, introduced by a tape velocity-dependent delay, e.g., introduced by the servo channel, between the modified lateral position estimate signal and an actual lateral position. The modified lateral position estimate may be used to modify a control signal sent to the actuator.

FIELD OF THE INVENTION

This disclosure relates generally to digital control systems, and inparticular to tape drive systems having a track-following servomechanismwith a predictor filter.

BACKGROUND

Since the 1950s, tape has persisted as the media of choice wheninexpensive and reliable data storage is required. The roles played bytape include data interchange, processing, and storage; today tapeserves generally as a media for archiving and backup. Progress in tapetechnology has resulted from substantial advances in channel, head,drive, and tape. Moreover, the cost of tape storage, normalized per unitcapacity (dollars per gigabyte), has decreased steadily over time drivenprimarily by advances in areal density and reduction in tape thickness.

Areal density is a two-dimensional measurement obtained as the productof linear density and track density. Linear density is a measure of howtightly bits are packed longitudinally along a length of tape. Increasesin linear density tend to lead to an increase inintersymbol-interference (ISI), unless corrected. Track density is ameasure of how tightly tracks are packed laterally on the tape.Increases in track density implies narrower track width, narrowerwrite/read heads, and closer head spacing, all of which tend to lead tolosses in signal-to-noise ratio (SNR), unless corrected. Increasinglinear densities beyond those achieved by state-of-the-art tape systemsis becoming difficult. Improving track density may therefore providefurther improvements in areal density.

BRIEF SUMMARY

Embodiments of the invention provide a track-following servomechanismfor a tape drive system, the servomechanism including: an actuatorcoupled to a head module housing at least one servo reader, the actuatorconfigured to actuate motion of the head module based on a controlsignal u(t); a servo channel coupled to the servo reader, the servochannel configured to receive from the servo reader a servo signal s(t)and configured to determine, based on the servo signal s(t), a lateralposition estimate signal y(t) representing a lateral position estimateof the servo reader and a tape velocity estimate signal v(t)representing longitudinal velocity of a tape, wherein the servo channelintroduces a tape velocity-dependent delay τ(v) into the lateralposition estimate signal y(t); a predictor filter coupled to the servochannel, the predictor filter configured to receive from the servochannel the lateral position estimate signal y(t) and the tape velocityestimate signal v(t), wherein the predictor filter determines a modifiedlateral position estimate signal ŷ(t) that reduces a difference,introduced by the tape velocity-dependent delay τ(v), between themodified lateral position estimate signal ŷ(t) and an actual lateralposition; and a compensator coupled to the predictor filter and theactuator, the compensator configured to modify the control signal u(t)based upon the modified lateral position estimate signal ŷ(t). Theservomechanism may also include a bypass route coupling the servochannel to the compensator, the bypass route bypassing the predictorfilter; and a switch coupled to the servo channel, the bypass route, andthe predictor filter, wherein the switch is configured to transmit thelateral position estimate signal y(t) along the bypass route when thetape velocity estimate signal v(t) indicates the velocity of the tape isat or above a threshold velocity and configured to transmit the lateralposition estimate signal y(t) to the predictor filter when the tapevelocity estimate signal v(t) indicates the velocity of the tape isbelow the threshold velocity. The predictor filter may be a Kalmanfilter.

Embodiments of the invention also provide a track-followingservomechanism for a tape drive system, the servomechanism including: adigital-to-analog converter (DAC) configured to receive a digitalcontrol signal u_(d)(t), convert the digital control signal u_(d)(t) toan analog control signal u_(a)(t), and output the analog control signalu_(a)(t); an actuator coupled to the DAC and coupled to a head modulehousing at least one servo reader, the actuator configured to receivefrom the DAC the analog control signal u_(a)(t) and to actuate motion ofthe head module based on the analog control signal u_(a)(t); a servochannel coupled to the servo reader, the servo channel configured toreceive from the servo reader a servo signal s(t), and the servo channelconfigured to output a lateral position estimate signal y(t)representing a lateral position estimate of the servo reader and a tapevelocity estimate signal v(t) representing longitudinal velocity of atape; a Kalman filter coupled to the servo channel, the Kalman filterconfigured to receive from the servo channel the lateral positionestimate signal y(t) and the tape velocity estimate signal v(t), and toreceive the digital control signal u_(d)(t), and the Kalman filterconfigured to output an estimate of an augmented actuator state signal{circumflex over (x)}_(aug)(t), and a modified lateral position estimatesignal ŷ(t); a controller coupled to the servo channel and the Kalmanfilter, the controller configured to receive from the servo channel thetape velocity estimate signal v(t) and receive from the Kalman filterthe estimate of the augmented actuator state signal {circumflex over(x)}_(aug)(t), and the controller configured to output an augmentedcontrol signal u_(aug)(t); a subtractor coupled to the Kalman filter,the subtractor configured to receive from the Kalman filter the modifiedlateral position estimate signal ŷ(t), and the subtractor configured tooutput a difference between a reference signal r(t) and the modifiedlateral position estimate signal ŷ(t) as a modified error signal ê(t); acompensator coupled to the subtractor, the compensator configured toreceive from the subtractor the modified error signal ê(t), and thecompensator configured to output a preliminary digital control signalu_(d0)(t); and an adder coupled to the compensator, the controller, theDAC, and the Kalman filter, the adder configured to receive from thecompensator the preliminary digital control signal u_(d0)(t) and fromthe controller the augmented control signal u_(aug)(t), and the adderconfigured to output to the DAC and to the Kalman filter the digitalcontrol signal u_(d)(t). The servo channel may be equivalent to afirst-order low-pass filter having a variable time constant that variesbased on a tape velocity-dependent delay τ(v).

Embodiments of the invention also provide a method for determiningparameters of a Kalman filter of a track-following servomechanism for atape drive system, the method including: identifying a particular tapevelocity above a threshold velocity; using the particular velocity,determining parameters of a proportional-integral-derivative (PID)compensator of a servomechanism; selecting a set of tape velocities,wherein each velocity in the set is less than or equal to the thresholdvelocity; and at each velocity in the set of tape velocities,determining parameters of a Kalman filter of the servomechanism based onthe parameters of the compensator. The threshold velocity may be 1.6m/s. The method may further include, when the servomechanism is in atape drive system having digital speed matching enabled, duringoperation of the servomechanism, selecting parameters for the Kalmanfilter based on linear interpolation for tape velocities betweenvelocities of the set.

Embodiments of the invention also provide a method for determiningparameters of a track-following servomechanism for a tape drive systemhaving a proportional-integral-derivative (PID) compensator, a Kalmanfilter, and a linear quadratic Gaussian (LQG) controller, the methodincluding: identifying a range of tape velocities; identifying a processnoise standard deviation from a corresponding lateral position outputfor all velocities within the range; identifying a measurement noisestandard deviation from a corresponding lateral position output for allvelocities within the range; identifying weighted norms thatcharacterize a deviation of an overall closed-loop response from adesired transfer characteristic, a contribution of process noise to alateral position signal, and a contribution of measurement noise to thelateral position signal; for a given velocity above a thresholdvelocity, determining parameters for a proportional-integral-derivative(PID) compensator that minimize a sum of the weighted norms; based on atape velocity-dependent delay τ(v), the process noise standarddeviation, and the measurement noise standard deviation, determiningparameters for a Kalman filter for each tape velocity within apredetermined set of tape velocities; and based on the tapevelocity-dependent delay τ(v), determining parameters for a linearquadratic Gaussian (LQG) controller for each tape velocity within apredetermined set of tape velocities. The range of tape velocities maybe 0.6 m/s-1.6 m/s.

Embodiments of the invention also provide a method for operating aservomechanism in a tape drive system, the method including: receiving aservo signal s(t) from a servo reader; based on the servo signal s(t),determining a lateral position estimate y(t) of the servo reader; basedon the servo signal s(t), determining a velocity estimate v(t) of a tapebeing read by the servo reader; identifying a tape velocity based on thevelocity estimate v(t); if the tape velocity is above a thresholdvelocity, feeding back the lateral position estimate y(t) to acompensator; if the tape velocity is below the threshold velocity,wherein the threshold velocity is a velocity at which a non-negligibletape velocity-dependent delay τ(v) is introduced into the lateralposition estimate signal y(t), transmitting the lateral positionestimate y(t) to a predictor filter, wherein the predictor filterdetermines a modified lateral position estimate signal ŷ(t) that reducesor minimizes a difference, introduced by the tape velocity-dependentdelay τ(v), between the modified lateral position estimate signal ŷ(t)and an actual lateral position, and transmitting the modified lateralposition estimate signal ŷ(t) to the compensator; and outputting fromthe compensator a control signal for an actuator coupled to the servoreader.

Embodiments of the invention further provide a digital control systemincluding: a sensor module including at least one sensor and anassociated parameter module, wherein the at least one sensor isconfigured to sense an attribute of a physical object, and wherein theassociated parameter module is configured to determine an observablesystem parameter associated with the physical object and affecting theattribute, and wherein the sensor module is configured to provide afeedback signal based on the attribute and a signal representing theobservable system parameter, and wherein the sensor module is tointroduce in the feedback signal a delay dependent on the observablesystem parameter; a predictor filter coupled to the sensor module, thepredictor filter configured to receive from the sensor module thefeedback signal and the signal representing the observable systemparameter, wherein the predictor filter is further configured todetermine a modified feedback signal that reduces a difference,introduced by the delay dependent on the observable system parameter,between the modified feedback signal and an actual physical attribute;and a compensator coupled to the predictor filter, the compensatorconfigured to modify a control signal u(t) based upon the modifiedfeedback signal. The predictor filter may be a Kalman filter. Theattribute of the physical object may be a position of the physicalobject and the observable system parameter associated with the physicalobject may be a velocity of the physical object.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the invention are described by way of example withreference to the accompanying drawings wherein

FIG. 1 is a schematic representation of a tape head and a segment of alinear data storage tape with a plurality of separate servo bands inaccordance with embodiments of the invention;

FIG. 2 is an illustration of a servo band in accordance with embodimentsof the invention;

FIG. 3 is an illustration of a pair of servo burst patterns inaccordance with embodiments of the invention;

FIG. 4 is a block diagram of a prior art track-following servomechanismfor a tape drive system;

FIG. 5 is a block diagram of a track-following servomechanism for a tapedrive system in a synchronous mode of operation in accordance withembodiments of the invention;

FIG. 6 is a graph illustrating a servo channel delay for a tape velocityof 1 m/s and a sinusoidal tape motion disturbance of 20 μm in amplitudeand 1 kHz in frequency;

FIG. 7 is a graph of servo channel delay versus time interval betweenlateral position estimates in accordance with embodiments of theinvention;

FIG. 8 is a diagram of a method for determining parameters of apredictor filter of a track-following servomechanism in accordance withembodiments of the invention;

FIG. 9 is a diagram of a method for determining parameters of atrack-following servomechanism in accordance with embodiments of theinvention;

FIGS. 10-12 are diagrams comparing the responses of a prior-arttrack-following servomechanism to a track-following servomechanismhaving an adjustable predictor in accordance to embodiments of theinvention; and

FIGS. 13-14 are diagrams comparing the performance of a prior-arttrack-following servomechanism to a track-following servomechanismhaving an adjustable predictor in accordance to embodiments of theinvention.

DETAILED DESCRIPTION OF THE INVENTION

Historically, tape has had to bear the burden of legacy products whilesemiconductor memory (SCM) and hard disk drives (HDD) faced no suchburden. In view of the legacy burden of tape, a Linear Tape-Open®†(LTO®) specification was designed to allow backward-compatibleimprovements. Linear data storage tape is a medium for storing typicallylarge amounts of data. In use, linear data storage tape includes aplurality of data tracks extending longitudinally (length-wise) alongthe tape. Common examples of linear data storage tape include magnetictape media and optical tape media. A tape head is employed for readingand/or writing data on the data tracks. The tape head is typicallyshared between various data tracks or groups of data tracks, and ismoved between tracks or groups of tracks in a lateral direction relativeto the tape. In magnetic tape media, the tape head typically includes anumber of separate elements which read and/or write data with respect toa number of parallel tracks. † Linear Tape-Open and LTO are registeredtrademarks of International Business Machines Corporation,Hewlett-Packard Corporation, and Seagate Corporation in the UnitedStates, other countries, or both.

The tape head is typically provided with one or more separate servo readtransducers, laterally offset from the read and/or write elements, so asto track follow a servo band. The servo read transducers enable the readand/or write elements of the tape head to be guided along the datatrack(s). The LTO adopted a timing-based servo (or timing basedservoing) (TBS) format for linear tape systems. Timing-based servoingrefers to a method in which duration between pulses from obliquelywritten patterns provides information used to determine a tape's lateraland longitudinal position relative to a head module. The TBS formatprovides for dedicated servo signals that can be viewed as pilot signalsfrom which both precise longitudinal position information and preciselateral position information can be extracted. The value of being ableto extract even more precise lateral position information increases astrack density increases. In optical tape media, an optical servo may beassociated with an individual data track or with a separate servo track.

In one embodiment of the invention, a track-following servomechanism fora tape drive system includes an actuator, a servo channel, a predictor(e.g., a Kalman filter), and a compensator. (Herein, the term“predictor” and “predictor filter” are used interchangeably.) Theactuator is coupled to a head module housing at least one servo reader.The head module houses the servo reader(s) by providing physical supportfor the servo reader(s), such as, for example, by having the servoreader(s) mounted on the head module, by protecting the servo reader(s)on two or more sides, and/or by having the servo reader(s) locatedwithin the head module. The servo reader is coupled to the servochannel, which is coupled to the predictor. The predictor is coupled tothe compensator, which couples back to the actuator. The actuator isconfigured to actuate motion of the head module based on a controlsignal u(t). The servo channel is configured to receive a servo signals(t) from the servo reader. The servo channel is configured todetermine, based on the servo signal s(t), a lateral position estimatesignal y(t) and a tape velocity estimate signal v(t). The lateralposition estimate signal represents a lateral position of the servoreader. The tape velocity estimate signal represents longitudinalvelocity of a tape being read/written by the tape drive system. Theservo channel introduces a tape velocity-dependent delay τ(v) into thelateral position estimate signal y(t). The predictor, which isconfigured to receive from the servo channel the lateral positionestimate signal y(t) and the tape velocity estimate signal v(t),determines a modified lateral position estimate signal ŷ(t) that reducesor minimizes the difference, introduced by the tape velocity-dependentdelay τ(v), between the modified lateral position estimate signal ŷ(t)and an actual lateral position. This modified lateral position estimatesignal ŷ(t) is provided to the compensator. The compensator modifies thecontrol signal u(t) based upon the modified lateral position estimatesignal ŷ(t).

Accordingly, the effects of the velocity-dependent delay τ(v) aremitigated by incorporation of a predictor (e.g., a Kalman filter) thatcan be readily optimized for certain applications by adjustingparameters of the predictor. As further described herein, in oneembodiment, a gain scheduling technique is used to determinecoefficients of the predictor in case of drive operations where avariable tape velocity is required, e.g., when digital speed matching isenabled. In certain embodiments, the predictor is also applied tomitigate effects of computational delays introduced by furtherprocessing of the lateral position estimates. Thus, embodiments of theinvention provide optimal prediction of an actuator state even in thepresence of a velocity-dependent delay that is introduced by a servochannel into lateral position estimates, and/or computational delaysintroduced by further processing of the lateral position estimates.Embodiments of the invention also provide a technique for operating aservomechanism in a tape drive system consistent with the above.

FIG. 1 is a schematic representation of a tape head and a segment of alinear data storage tape with a plurality of separate servo bands inaccordance with embodiments of the invention. FIG. 1 shows a linear datastorage tape 100 and a tape head 120. The linear data storage tape 100has a plurality of separate longitudinal servo bands 140, 141, 142, 143and 144, laterally positioned on the linear data storage tape. The tapehead 120 includes a number of separate read and/or write elements 122and two separate servo transducers 124 and 125 which are laterallyoffset (along the y-axis) from the read and/or write elements 122. Inuse, each of the servo transducers 124, 125 track follows a servo track(or servo path) along one of the servo bands (e.g., band 140 and 141)while the elements 122 read and/or write data with respect to a numberof data tracks (not shown) positioned between the servo bands.

FIG. 2 is an illustration of a servo band (e.g., servo band 140) inaccordance with embodiments of the invention. In FIG. 2, a servo bandcenter line 210 and two pairs of servo bursts 202 and 204 are shown. “ABurst” and “B Burst” make up the servo burst pair 202. “C Burst” and “DBurst” make up the servo burst pair 204. The servo bursts in one pairare written on tape at an angle relative to each other. For example, ABurst is at an angle relative to B Burst. In application, a servotransducer (e.g., 124) is configured to move longitudinally relative tothe tape (e.g., along the x-direction identified in FIG. 1) in a mannerso as to keep a constant value for the distance between the bursts(e.g., x₀ between A Burst and B Burst, and x₁ between C Burst and DBurst). In this way, the servo transducer follows a straight line withinthe servo band. Any small deviation away from the correct path causes avariation (plus or minus) in the gap between the bursts. Thisconfiguration allows for head lateral position and tape velocityestimates to be derived from the relative timing of pulses generated bya servo reader reading the servo bursts. In many applications, two servobands (e.g., 140 and 141) are used simultaneously to provide two sourcesof servo information for increased accuracy. In those applications, twoservo readers are active at all times to read two dedicated servochannels. Longitudinal tape position as well as lateral head positioninformation may be derived from each servo channel.

In TBS systems, recorded servo patterns have transitions with twodifferent slopes such as shown in FIG. 2. The current TBS formatspecifies several nominal servo positions parallel to the servo bandcenter line, e.g., 210. The nominal servo positions serve as referencewithin each servo band for the track-following system. Each generationof LTO drives is characterized by a specific number of nominal servopositions, and hence by a specific number of tracks within a data band.Accordingly, this technology can be very finely tuned and is capable ofsupporting very high track densities using the same servo tracks becausethe nominal positions are not fixed servo tracks but instead definitionsof different “x distances” (or sets of “x distances”) between servobursts.

FIG. 3 is an illustration of a pair of servo burst patterns inaccordance with embodiments of the invention. Lateral position estimatesare generated by a servo channel processing a signal s(t) from a servoreader. In FIG. 3, the rate at which the lateral position estimates aregenerated is equal to the velocity v of the tape divided by the distance(in this case, 100 μm) between servo burst pairs. The lateral positioninformation is used to determine a position-error-signal (PES), which intape drive systems is provided as input to a compensator of atrack-following servomechanism. In FIG. 3, longitudinal position (LPOS)information was encoded using pulse-position modulation (PPM)techniques. The pulse-position modulation for the encoding of the LPOSinformation is indicated in the A and B bursts of FIG. 3 as an “LPOSmodulation” of +/−0.25 μm.

FIG. 4 is a block diagram of a prior art track-following servomechanismfor a tape drive system. The servomechanism 400 is based on aproportional-integral-derivative (PID) compensator 402 in asynchronousmode of operation. The servomechanism 400 includes the PID compensator402, a digital-to-analog converter (DAC) 404, an actuator 406, a headmodule 407, at least one servo reader 408 located in or on the headmodule 407, a servo channel 410, a rate converter 412, and a subtractor440. FIG. 4 also shows various disturbances that are often present intape drive systems (e.g., shocks, vibrations, stack shifts, andnarrowband disturbances). FIG. 4 further shows a signal s(t) provided bythe servo reader to the servo channel, a tape velocity estimate signalv(t_(n)), lateral position estimate signals y(t_(n)) and y(t_(k)), atime signal t_(k), a reference signal r(t_(k)), a position error signal(PES) e(t_(k)), and control signals u_(digital) and u_(analog).

In use, the servomechanism 400 uses the PES e(t_(k)) as an input to thePID compensator 402. The compensator 402 outputs a digital controlsignal u_(digital) to the DAC 404. The DAC 404, operating at a fixedsampling rate f_(s) in asynchronous mode of operation, converts thedigital control signal u_(digital) to an analog signal u_(analog) andoutputs the analog signal. The actuator 406 receives the analog controlsignal u_(analog). Based on the control signal, the actuator adjusts theposition of the head module 407, which in turn determines positions ofthe servo reader 408 and corresponding read/write heads (not shown). Theread/write heads are maintained at a desired “on track” position viamotion of the actuator and also via feedback provided by the servoreader 408. Specifically, the servo reader 408 provides a signal s(t) tothe servo channel 410. The servo channel 410 processes the signal s(t)to generate a lateral position estimate, provided as the signaly(t_(n)), and a signal v(t_(n)) indicating an estimate of the velocityof the tape being read/written.

The rate at which the lateral position estimates are generated dependson the velocity of the tape. In the configuration shown in FIG. 4, therate converter 412 converts the rate at which the lateral positionestimates are generated (in this case at instants t_(n)) to the fixedsampling rate f_(s) of the DAC (that is to instants t_(k)). Theconversion is performed prior to using the lateral position estimatesand the reference signal r(t_(k)) to determine the PES e(t_(k)), andprior to providing the PES to the PID compensator. Thus, theservomechanism 400 is considered to be in an asynchronous mode ofoperation. In a synchronous mode of operation, the rate at which thelateral position estimates are generated is equal to the DAC samplingrate f_(s), and no rate conversion is performed.

In TBS systems (including the one shown in FIG. 4), the servo channel(e.g., 410) introduces a time-varying delay, specifically a tapevelocity-dependent delay, into the estimation of the lateral position. Adelay in the feedback of a closed-loop system, e.g. the system shown inFIG. 4, translates into a reduced phase margin, and hence into a highersensitivity to both process noise and measurement errors. The tapevelocity-dependent delay is non-negligible on the performance of thetrack-following servomechanism at tape velocities below approximately 2m/s. Currently, tape velocities of possibly 1.6 m/s for read/writeoperations in commercial tape drives are being considered, with tapevelocities of 1 m/s and lower possibly being eventually supported.

One technique of compensating for a time delay is through use of a Smithpredictor. In such a technique, the delayed output is predicted using aplant model and a delay time model. Then, by using the predictiveoutput, the time delay can be reduced in a closed-loop configuration.The use of a Smith predictor can be extended to state space, where itmay be referred to as state predictive control. However, when the timedelay cannot be reliably estimated (e.g., due to variable velocities ormodel inaccuracies), a significant error arises between the delay timemodel in the Smith predictor and the actual delay time. This leads toimpaired loop stability and performance.

Embodiments of the invention provide a method and system for mitigatingeffects of a feedback delay that is dependent on an observable systemparameter. Embodiments of the invention incorporate an adjustablepredictor (e.g., a Kalman filter) to mitigate the effects of thetime-varying delay introduced by the servo channel in tape drivesystems. Parameters of the predictor can be adjusted to optimize forcertain conditions, including for example, operation of the tape drivesystem at tape velocities of less than 2.0 m/s, e.g., in the range of0.6-1.6 m/s, in the range of 0.4-1.4 m/s, in the range of 0.8-1.2 m/s,or a range of 1.0-1.8 m/s.

FIG. 5 is a block diagram of a track-following servomechanism 500 for atape drive system in a synchronous mode of operation in accordance withembodiments of the invention. In FIG. 5 discrete-time operation of thetrack-following loop is assumed, where estimates v(t_(k)) and y(t_(k))are computed at time instants t_(k)=k 100 μm/v. The track-followingservomechanism 500 mitigates effects of a delay in a lateral positionestimate introduced by a servo channel. The delay is dependent on tapevelocity. Accordingly, the delay is, and/or during simulation is modeledas, a function of the tape velocity and expressed herein as τ(v).

The servomechanism 500 includes a compensator 502, a digital-to-analogconverter (DAC) 504, an actuator 506, a head module 507, at least oneservo reader 508 located in or on the head module 507, a servo channel510, a predictor 520, a controller 530, a subtractor 540, and an adder560. FIG. 5 also shows various disturbances often present in tape drivesystems (e.g., shocks, vibrations, stack shifts, and narrowbanddisturbances). FIG. 5 further shows a signal s(t) provided by the servoreader 508 to the servo channel 510, a tape velocity estimate signalv(t_(k)), lateral position estimate signals y(t_(k)) and ŷ(t_(k)), astate signal {circumflex over (x)}_(aug)(t_(k)), a reference signalr(t_(k)), a position error signal (PES) ê(t_(k)), and control signalsu_(d0)(t_(k)), u_(aug)(t_(k)), u_(d)(t_(k)), and u_(a)(t).

In FIG. 5, the DAC 504 operates at a sampling rate of f_(s) and isconfigured to receive a digital control signal u_(d)(t_(k)), convert thedigital control signal u_(d)(t_(k)) to an analog control signalu_(a)(t), and output the analog control signal u_(a)(t). The actuator506 is coupled to the DAC 504 and also coupled to the head module 507.The head module 507 houses (provides physically support for) at leastone servo reader (e.g., 508). The actuator 506 is configured to receivefrom the DAC 504 the analog control signal u_(a)(t) and actuate motionof the head module 507, and therefore the servo reader 508, based on theanalog control signal u_(a)(t). In one embodiment, the actuator 506 isconfigured to receive from the servo reader 508 a servo signal s(t), asshown in FIG. 5 by the dashed arrows.

The servo channel 510 is coupled to the servo reader 508. The servochannel 510 is configured to receive the servo signal s(t) and output alateral position estimate signal y(t_(k)) and a tape velocity estimatesignal v(t_(k)). The lateral position estimate signal y(t_(k))represents a lateral position estimate of the servo reader 508 andaccordingly may also be used to represent a lateral position estimate ofthe head module 507. The tape velocity estimate signal v(t_(k))represents a longitudinal velocity (e.g., 0.6 m/s-⅙ m/s) of a tape(e.g., 100). The servo channel 510 introduces a tape velocity-dependentdelay τ(v) into the lateral position estimate signal y(t_(k)). Incertain embodiments, the servo channel 510 is equivalent to (and/orduring simulation is modeled as) a first-order low-pass filter having avariable time constant given by the delay τ(v). In one embodiment, thisvariable time constant varies based on the delay τ(v).

The predictor 520 is coupled to the servo channel 510. In oneembodiment, the predictor 520 is a Kalman filter (sometimes referred toas a Kalman predictor). The predictor 520 is configured to receive fromthe servo channel 510 the lateral position estimate signal y(t_(k)) andthe tape velocity estimate signal v(t_(k)). The predictor 520 is alsoconfigured to receive from the adder 560 a digital control signalu_(d)(t_(k)). The predictor 520 is further configured to output anestimate of an augmented actuator state signal {circumflex over(x)}_(aug)(t_(k)) (as described further below), and a modified lateralposition estimate signal ŷ(t_(k)).

The controller 530 is coupled to the servo channel 510 and the predictor520. In one embodiment, the controller is a linear quadratic Gaussian(LQG) controller. The controller 530 is configured to receive from theservo channel 510 the tape velocity estimate signal v(t_(k)). Thecontroller 530 is also configured to receive from the predictor 520 theestimate of the augmented actuator state signal {circumflex over(x)}_(aug)(t_(k)). The controller 530 is configured to output anaugmented control signal u_(aug)(t_(k)), which is received by the adder560.

The subtractor 540 is coupled to the predictor 520 and configured toreceive from the predictor 520 the modified lateral position estimatesignal ŷ(t_(k)). The subtractor 540 is also configured to output thedifference between a reference signal r(t_(k)) and the modified lateralposition estimate signal ŷ(t_(k)). The subtractor 540 outputs thisdifference as a modified position error signal ê(t_(k)).

The compensator 502 is coupled to the subtractor 540. In one embodiment,the compensator is a proportional-integral-derivative (PID) compensator.The compensator 502 is configured to receive from the subtractor 540 themodified position error signal ê(t_(k)). The compensator 502 outputs apreliminary digital control signal u_(d0)(t_(k)).

The adder 560 is coupled to the compensator 502, the controller 530, theDAC 504, and the predictor 520. The adder 560 is configured to receivefrom the compensator 502 the preliminary digital control signalu_(d0)(t_(k)). The adder 560 is also configured to receive from thecontroller 530 the augmented control signal u_(aug)(t_(k)). The adder isconfigured to output to the DAC 504 and to the predictor 520 the digitalcontrol signal u_(d)(t_(k)).

In use, the servo signal s(t) is received from the servo reader 508.Based on the servo signal s(t), a lateral position estimate signaly(t_(k)) of the servo reader is determined (e.g., by servo channel 510).Also based on the servo signal s(t), the estimated velocity signalv(t_(k)) of the tape (e.g., 100), which represents a longitudinalvelocity of the tape, is determined (e.g., by the servo channel 510).The estimated velocity signal v(t_(k)) and the lateral position estimatesignal y(t_(k)) are transmitted to the predictor 520. The predictordetermines a modified lateral position estimate signal ŷ(t_(k)) thatreduces or minimizes the difference, introduced by the tapevelocity-dependent delay τ(v), between the modified lateral positionestimate signal ŷ(t_(k)) and an actual lateral position. The modifiedlateral position estimate signal ŷ(t_(k)) is then provided to thecompensator 502, in FIG. 5 by way of the subtractor 540. In FIG. 5, themodified lateral position estimate signal ŷ(t_(k)) is provided to thecompensator 502 after being adjusted based on a reference signalτ(t_(k)). The subtractor 540 performs the adjustment and provides theadjusted signal as the error signal ê(t_(k)) to the compensator 502. Thecompensator 502 uses the modified error signal ê(t_(k)), which is basedon the modified lateral position estimate signal ŷ(t_(k)), to adjust itsoutput signal (e.g., u_(d0)(t_(k))) such that the control signals (e.g.,u_(d)(t_(k)) and u_(a)(t)), upon which the motion of the actuator andtherefore the head module is based, are modified. Accordingly, based onthe error signal, the compensator 502 outputs a control signal to theactuator 506 (e.g., via the adder 560 and the DAC 504).

In the embodiment shown in FIG. 5, the mechanical behavior of theactuator may be approximated by a simple spring-damper-mass model.Accordingly, the actuator can be represented by the second-orderdifferential equation:m{umlaut over (x)}(t)+b{dot over (x)}(t)+kx(t)=externally appliedforce+disturbances =gu(t)+d(t)  (1)wherein x(t) represents the position of the actuator, the firstderivative {dot over (x)}(t) of the position indicates the actuator'svelocity, the second derivative {umlaut over (x)}(t) of the positionindicates the actuator's acceleration, m represents the mass of theactuator, b represents a damping coefficient, and k represents a springconstant. The externally applied force is represented by the product ofa transducer gain g and the control signal u(t). The disturbances, dueto shocks and vibrations for example, are represented by d(t). Bydefining the state vector of the actuator as

$\begin{matrix}{{{x(t)} = {\begin{bmatrix}{x(t)} \\{\overset{.}{x}(t)}\end{bmatrix} = \begin{bmatrix}{position} \\{velocity}\end{bmatrix}}},} & (2)\end{matrix}$the differential equation (1) representing the actuator may be expressedin state-space form as

$\begin{matrix}{{\overset{.}{x}(t)} = {{\begin{bmatrix}0 & 1 \\{{- k}/m} & {{- b}/m}\end{bmatrix}{x(t)}} + {\begin{bmatrix}0 \\{g/m}\end{bmatrix}{u(t)}} + {\begin{bmatrix}0 \\{1/m}\end{bmatrix}{{d(t)}.}}}} & (3)\end{matrix}$

When the servo channel is equivalent to (or can be substantially treatedas) a first-order low-pass filter having a variable time constant thatvaries based on the delay τ(v), the dynamics of an augmented system(approximating the combined actuator and servo channel) are described by

$\begin{matrix}{{{{\overset{.}{x}}_{aug}(t)} = {{\begin{bmatrix}0 & 1 & 0 \\{{- k}/m} & {{- b}/m} & 0 \\{1/{\tau(v)}} & 0 & {1/{\tau(v)}}\end{bmatrix}{x_{aug}(t)}} + {\begin{bmatrix}0 \\{g/m} \\0\end{bmatrix}{u(t)}} + {\begin{bmatrix}0 \\{1/m} \\0\end{bmatrix}{d(t)}}}},} & (4)\end{matrix}$

where the state vector of this augmented system is defined as

$\begin{matrix}{{x_{aug}(t)} = {\begin{bmatrix}{x(t)} \\{x_{lpf}(t)}\end{bmatrix} = {\begin{bmatrix}{{actuator}\mspace{14mu}{state}} \\{{low}\text{-}{pass}\mspace{14mu}{filter}\mspace{14mu}{state}}\end{bmatrix}.}}} & (5)\end{matrix}$

The output signal of the augmented system (i.e., the combined actuatorand servo channel) is given by the lateral position estimates outputtedby the servo channel. This output can be expressed in terms of a statevector asy(t)=[001]x _(aug)(t)+w(t),  (6)where w(t) represents the measurement error due to, for example, stackshifts, narrowband disturbances representing lateral tape motion, andadditive stationary and nonstationary noise affecting the servo channelsignal. The predictor (e.g., a Kalman filter) mitigates effects of thetape velocity dependent delay on the system by estimating the state ofthe augmented system given by the cascade of such a second-orderactuator and such a first-order servo channel.

The velocity-dependent delay τ(v) may be better understood byconsidering a disturbance in tape motion. One type of disturbance issinusoidal lateral tape motion. FIG. 6 is a graph illustrating a servochannel delay for a tape velocity of 1 m/s and a sinusoidal tape motiondisturbance of 20 μm in amplitude and 1 kHz in frequency. In the case ofsinusoidal lateral tape motion disturbances with a slew rate of up to0.1 m/s and an amplitude within the range of the actuator stroke, theservo channel delay is essentially independent of the disturbanceamplitude and frequency in the frequency band where the servo channeloperates (which is in the order of a few kHz).

FIG. 7 is a graph of servo channel delay versus time interval betweenlateral position estimates in accordance with embodiments of theinvention. In FIG. 7, the abscissa is given by the time interval betweenconsecutive lateral position estimates. For tape velocities in the rangewhere the servo channel delay is non-negligible and read/writeoperations for future LTO drive generations are envisioned (e.g.,approximately 0.6 m/s-1.6 m/s), the delay is approximately inverselyproportional to velocity. For servo patterns such as in FIG. 3, thedependency of the delay (expressed in milliseconds) on velocity(expressed in m/s) can be represented by the approximation

$\begin{matrix}{{{\tau(v)} = {\frac{c}{v} \approx \frac{62}{v}}},} & (7)\end{matrix}$where c is a constant of proportionality obtained, in the case above, byobserving the servo channel delay for a tape velocity of 1 m/s (which isbetween 0.6 m/s and 1.6 m/s). When the tape velocity is 1 m/s, theconstant of proportionality c is 62, as understood by examining FIG. 7.

In certain embodiments, the predictor is configured to determine theestimate of the augmented actuator state signal {circumflex over(x)}_(aug)(t) and the modified lateral position estimate signal ŷ(t) atdiscrete time instants such that the modified lateral position estimatesignal can be expressed as ŷ(t_(k)). In synchronous mode of operation,the discrete time instants t_(k) are equal to an integer k times asampling interval T of the DAC, where T=1/f_(s). In FIG. 5, the samplingrate f_(s) of the DAC 504 is synchronous with the rate at which theservo channel generates the lateral position estimates. Thus, whenreading/writing to a tape having servo patterns such as those shown inFIG. 3, the rate of generation of the lateral position estimates isgiven by

$\begin{matrix}{{{rate}\mspace{14mu}{of}\mspace{14mu}{lateral}\mspace{14mu}{position}\mspace{14mu}{estimates}\mspace{14mu}{generation}} = \frac{{velocity}\mspace{14mu}{of}\mspace{14mu}{tape}}{100\mspace{14mu}{µm}}} & (8)\end{matrix}$According, the sampling interval T of the DAC 504 would be

$\begin{matrix}{T = {\frac{1}{f_{s}} = \frac{100\mspace{14mu}{µm}}{{velocity}\mspace{14mu}{of}\mspace{14mu}{tape}}}} & (9)\end{matrix}$since the servomechanism is in synchronous mode of operation (i.e., therate at which the lateral position estimates are generated is equal tothe DAC sampling rate f_(s), and no rate conversion is performed.) Inanother embodiment, the servomechanism is in an asynchronous mode ofoperation. In such an embodiment, a rate converter (e.g., 512) may bepositioned to receive the lateral position estimates from the servochannel (e.g., y(t_(n))) and convert the rate at which the lateralposition estimates are generated to the fixed sampling rate f_(s) of theDAC, outputting y(t_(k)).

For each tape velocity in a set of target velocities, the state-spacerealization of the track-following servomechanism may be obtained by anoptimization procedure that reduces or minimizes the contribution ofprocess noise and measurement noise to the output lateral position. Inapplications where the standard deviations of both process noise andmeasurement noise are known for the target velocities, this proceduremay include the following operations.

First, for a given velocity at which the servo channel delay isnegligible (e.g., >2.0 m/s), parameters of the compensator (e.g., a PIDcompensator) are identified which minimize the sum of weighted norms.The weighted norms characterize the deviation of the overall closed-loopresponse from a desired transfer characteristic, as well as thecontributions of process and measurement noise to the output y-position(e.g., ŷ(t_(k))).

Then, while maintaining the compensator parameters identified,parameters for the predictor (e.g., a Kalman filter) and the controller(e.g., the LQG controller) are identified at each of the targetvelocities within the set (e.g., a predetermined set of velocitieswithin the range of 0.6 m/s-1.6 m/s or other ranges). In certainembodiments, these parameters are identified based on equation (4) whichrepresents the dynamics of the augmented system, and equation (6) whichrepresents the output signal of the augmented system in terms of a statevector.

FIG. 8 is a diagram of a method 800 for determining parameters of apredictor filter of a track-following servomechanism in accordance withembodiments of the invention. At operation 802, a particular tapevelocity above a threshold velocity (e.g., 1.6 m/s) is identified. Atoperation 804, using the particular velocity, parameters of acompensator (e.g., a PID compensator of a track-followingservomechanism) are determined. At operation 806, a set of tapevelocities is selected. Each velocity in the set is less than or equalto the threshold velocity. For example, if the threshold velocity is 1.6m/s, the set of tape velocities may be {0.6 m/s; 0.8 m/s; 1.0 m/s; 1.2m/s; 1.4 m/s}. At operation 808, parameters of a predictor of theservomechanism are determined at each velocity in the set of tapevelocities based on the parameters of the compensator. At operation 810,the method ends. In use, the operations 802-810 may be applied as anoptimization technique.

In certain applications, a gain scheduling approach is adopted todetermine coefficients of the predictor in case of drive operationswhere variable tape velocities occur, such as when the predictor is partof a servomechanism in a tape drive system having digital speedmatching. Digital speed matching adjusts throughput under slow orvarying host data transfer rate conditions. Digital speed matching isintended to mitigate performance inconsistency problems in systems inwhich the tape drive delivers throughput that is sufficiently high suchthat other system components (e.g., the operating system, host adapters,servers, and disk subsystems) have difficulty keeping up with thestreaming performance capabilities. Digital speed matching reduces thenumber of repositions and improves throughput performance. Since incertain embodiments the servo channel provides nearly instantaneousestimates of tape velocity, linear interpolation can be used to obtainparameters (e.g., coefficients) of the predictor and controller fairlyaccurately. Accordingly, in applications in which digital speed matchingis enabled, parameters of the Kalman filter and of the controller may beconsidered to vary linearly between the parameter values obtained forthe finite set of tape velocities (e.g., at operation 808).

Accordingly, in one embodiment, the method 800 may further includeoperation 812, at which it is determined if the servomechanism is in atape drive system having digital speed matching enabled. This may beaccomplished statically or dynamically at run-time by reading orotherwise checking a flag or a jumper for example. Then, at operation814, during operation of the servomechanism, for tape velocities betweenvelocities of the set, parameters are selected for the predictor basedon linear interpolation. In certain embodiments, parameters are alsoselected for the controller based on linear interpolation, e.g., also atoperation 814.

FIG. 9 is a diagram of a method 900 for determining parameters of atrack-following servomechanism in accordance with embodiments of theinvention. At operation 902, a range of tape velocities is identified.At operation 904, a standard deviation due to process noise from acorresponding lateral position output is identified for all velocitieswithin the range. At operation 906, a standard deviation due tomeasurement noise from a corresponding lateral position output isidentified for all velocities within the range. At operation 908,weighted norms that characterize a deviation of an overall closed-loopresponse from a desired transfer characteristic, a contribution ofprocess noise to a lateral position signal, and a contribution ofmeasurement noise to the lateral position signal are identified. Atoperation 910, for a given velocity above a threshold velocity (e.g.,1.6 m/s), parameters for a compensator that minimize a sum of theweighted norms are determined. At operation 912, parameters for apredictor for each tape velocity within a predetermined set of tapevelocities are determined based on a tape velocity-dependent delay τ(v),the process noise standard deviation, and the measurement noise standarddeviation. At operation 914, parameters for a controller for each tapevelocity within a predetermined set of tape velocities are determinedbased on the tape velocity-dependent delay τ(v). In one embodiment, thecompensator is a proportional-integral-derivative (PID) compensator, thepredictor is a Kalman filter, and the controller is a linear quadraticGaussian (LQG) controller. In one embodiment, the threshold velocity isabove 1.6 m/s and each tape velocity within the predetermined set oftape velocities is between 0.6 m/s-1.6 m/s, inclusive.

By using a Kalman filter as the predictor filter, a combined plant andideal servo channel with constant delay can be approximated. For a giventape velocity v, steady-state equations for a Kalman filter may beexpressed as{circumflex over (x)} _(aug,k) = x _(aug,k) +L(y(t)−H x_(aug,k))(measurement update)  (10)andx _(aug,k+1) =F x _(aug,k) +Gu _(k), (time update)  (11)wherein y(t) is the lateral position estimate signal from the servochannel at discrete time instants k, L is a 3×1 matrix that representsan innovation gain of the Kalman filter, F is a 3×3 matrix, G is a 3×1matrix, and H is a 1×3 matrix, and wherein the matrices F, G, and H givea discrete-time state-space representation of the servomechanism. Incertain embodiments, L depends on τ,σ_(d) ²,σ_(w) ², and v, wherein τ isthe delay, σ_(d) is variance of process noise, and σ_(w) is variance ofmeasurement noise, and therefore may be expressed as L(τ,σ_(d) ²,σ₂ ²;v). The tape velocity v is also indicated as a variable since, ingeneral, the servo channel delay, the process noise variance, and themeasurement noise variance all depend on tape velocity. Accordingly, inone embodiment, the Kalman filter is configured to determine an estimateof the augmented actuator state signal {circumflex over (x)}_(aug)(t)using equations (10) and (11). The Kalman filter also may be configuredto provide a refinement of the lateral position estimate, given by:ŷ(t _(k))=H{circumflex over (x)} _(aug)(t _(k))  (12)

FIGS. 10-12 are diagrams comparing the loop frequency, process noisefrequency, and measurement-noise frequency responses of a prior-arttrack-following servomechanism (as shown in FIG. 4 for asynchronous modeof operation) to a track-following servomechanism having an adjustablepredictor in accordance to embodiments of the invention. Specifically,FIG. 10( a) shows overall track-following loop frequency responsewithout a predictor (as in FIG. 4) for v=1 m/s. FIG. 10( b) showsoverall track-following loop frequency response with a predictor inaccordance with embodiments of the invention for v=1 m/s. FIG. 11( a)shows process noise frequency response without a predictor for v=1 m/s.FIG. 11( b) shows process noise frequency response with a predictor forv=1 m/s. FIG. 12( a) shows measurement-noise frequency response withouta predictor for v=1 m/s. FIG. 12( b) shows measurement-noise frequencyresponse with a predictor for v=1 m/s.

Performance comparisons for entire track-following servomechanisms weremade for tape velocities in the range of 0.6-1.6 m/s, inclusive,including actuators and compensators currently implemented in LTO-4drives. FIGS. 13-14 are diagrams comparing the performance of aprior-art track-following servomechanism (as shown in FIG. 4 forasynchronous mode of operation) to a track-following servomechanismhaving an adjustable predictor in accordance to embodiments of theinvention (such as shown in FIG. 5 for synchronous mode of operation).

FIG. 13 shows a comparison of the performance of an asynchronoustrack-following servomechanism without and with a predictor. As seen inFIG. 13, the servomechanism with the predictor in accordance withembodiments of the invention has a relatively stable position errorsignal (PES) standard deviation compared to a servomechanism without thepredictor. The PES standard deviation for the servomechanism without thepredictor increases approximately exponentially as the velocitydecreases below 1.6 m/s.

FIG. 14 shows a comparison of the performance of a synchronoustrack-following servomechanism without and with a predictor. As seen inFIG. 14, at lower tape velocities (e.g., ≦1.6 m/s), the track-followingservomechanism with a predictor has a smaller PES standard deviationthan the track-following servomechanism without a predictor.

In certain embodiments, the servomechanism is configured to operatedifferently depending on the velocity of the tape. For example, in oneembodiment, the servomechanism includes a bypass route and switch. Thebypass route couples the servo channel to the compensator and enables alateral position estimate signal to be transmitted from the servochannel to the compensator, bypassing the predictor. The switch iscoupled to the servo channel, the bypass route, and the predictor. Theswitch switches between, for example, transmitting the lateral positionestimate signal y(t_(k)) from the servo channel 510 to the predictor 520to transmitting the signal y(t_(k)) from the servo channel 510 to thecompensator 502 via the bypass route. In this embodiment, theservomechanism is configured so that the switch is configured totransmit in one instance the lateral position estimate signal y(t_(k))along the bypass route when the tape velocity estimate signal v(t_(k))is at or above (or indicates that the velocity of the tape is at orabove) a threshold velocity, and to transmit, in another instance, thesame signal y(t_(k)) to the predictor when the tape velocity estimatesignal v(t_(k)) is below (or indicates the velocity of the tape isbelow) the threshold velocity. In the context of this tape-drive systemembodiment, the threshold velocity is the velocity at which anon-negligible tape velocity-dependent delay τ(v) is introduced, e.g.,non-negligibly by the servo channel, into the lateral position estimatesignal. In one embodiment, this threshold velocity is 1.6 m/s.

Accordingly, a servomechanism in accordance with certain embodiments ofthe invention may operate as follows: A servo signal is received from aservo reader. Based on the servo signal, a lateral position estimate isdetermined and a tape velocity estimate is determined. If the tapevelocity estimate indicates that the tape velocity is above a thresholdvelocity (e.g., >2.0 m/s, >1.6 m/s, or >1.4 m/s), the lateral positionestimate is transmitted (e.g., via the bypass route) to a compensator(e.g., a PID compensator). If the tape velocity estimate indicates thatthe tape velocity is at or below the threshold velocity (e.g., ≦2.0 m/s,≦1.6 m/s, or ≦1.4 m/s), the lateral position estimate is transmitted toa predictor filter (e.g., a Kalman filter). The predictor filterdetermines a modified lateral position estimate signal that reduces orminimizes the difference, introduced by the tape velocity-dependentdelay, between the modified lateral position estimate signal and anactual lateral position. The modified lateral position estimate signalis then transmitted to the compensator 502 (FIG. 5). Based on themodified lateral position estimate signal, the compensator outputs acontrol signal for the actuator 506, which is coupled to the servoreader 508.

As is understood from the above description, embodiments of theinvention are not limited to a tape drive system. Embodiments of theinvention may encompass generally a digital control system where asensor introduces a delay in a feedback, the delay depending on anobservable system parameter. For example, embodiments of the inventionprovide for a digital control system that includes a sensor module, apredictor filter (e.g., a Kalman filter (standard, modified, orextended), a predictor filter based on double exponential smoothing, atwo dimension self-learning predictor filter, a Recursive Total LeastSquares Filter, etc.) coupled to the sensor module, and a compensatorcoupled to the predictor filter.

The sensor module includes at least one sensor and an associatedparameter module. The sensor is configured to sense an attribute of aphysical object. For example, the attribute may be a position of theobject. In a tape drive system, the position may be, for example, theposition of a tape relative to a head module. In another application,the attribute may be, for example, a temperature of an object. Theassociated parameter module is configured to determine an observablesystem parameter associated with the physical object and affecting theattribute. For example, the associated parameter module may beconfigured to determine a velocity of the object. The velocity of anobject affects its position. As another example, the associatedparameter module may be configured to determine how long the object hasbeen powered on or operating, which in certain systems affects thetemperature of some objects.

The sensor module is configured to provide a feedback signal based onthe attribute (e.g., position or temperature) and a signal representingthe observable system parameter (e.g., velocity or operating time). Thesensor module introduces in the feedback signal a delay dependent on theobservable system parameter (e.g., velocity or operating time).

The predictor is configured to receive from the sensor module thefeedback signal and the signal representing the observable systemparameter. The predictor is further configured to determine a modifiedfeedback signal that reduces or minimizes the difference, introduced bythe delay dependent on the observable system parameter, between themodified feedback signal and an actual physical attribute. The predictoris configured to be adjustable, e.g., by having operating parametersthat can be varied. The compensator is configured to modify a controlsignal u(t) based upon the modified feedback signal.

Conclusion

Thus, a digital control system having a sensor that introduces a delayin a feedback, the delay depending on an observable system parameter, isdescribed, and in particular, a tape drive system having atrack-following servomechanism with a predictor mitigating effects ofdelay in feedback is described. The description of embodiments of theinvention has been presented for purposes of illustration anddescription, but is not intended to be exhaustive or limited to theinvention in the form disclosed. Many modifications and variations willbe apparent to those of ordinary skill in the art without departing fromthe scope and spirit of the invention. The embodiments were chosen anddescribed in order to best explain the principles of the invention andthe practical application, and to enable others of ordinary skill in theart to understand the invention for various embodiments with variousmodifications as are suited to the particular use contemplated.

The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting of the invention. Asused herein, the singular forms “a”, “an” and “the” are intended toinclude the plural forms as well, unless the context clearly indicatesotherwise. It will be further understood that the terms “comprises”and/or “comprising,” when used in this specification, specify thepresence of stated features, integers, steps, operations, elements,and/or components, but do not preclude the presence or addition of oneor more other features, integers, steps, operations, elements,components, and/or groups thereof. Further, references to “a method” or“an embodiment” throughout are not intended to mean the same method orsame embodiment, unless the context clearly indicates otherwise;references to “embodiments” throughout are not intended to mean allembodiments; and references to a “module” throughout are not intended tomean the same module, unless the context clearly indicates otherwise.

As will be appreciated by one skilled in the art, aspects of embodimentsof the invention may be embodied as a method, system, or computerprogram product. Accordingly, embodiments of the invention may take theform of an entirely hardware embodiment, or an embodiment combiningsoftware (including firmware, resident software, micro-code, etc.) andhardware aspects that may all generally be referred to herein as a“circuit,” “module” or “system.” Furthermore, certain aspects ofembodiments of the invention may take the form of a computer programproduct on a computer-usable storage medium having computer-usableprogram code embodied in the medium.

The flowchart and block diagrams in the figures illustrate thearchitecture, functionality, and operation of possible implementationsof systems, methods and computer program products according to variousembodiments of the invention. In this regard, each block in theflowchart or block diagrams may represent a module, segment, or portionof code, which comprises one or more executable instructions forimplementing the specified logical function(s). It should also be notedthat, in some alternative implementations, the functions noted in theblock may occur out of the order noted in the figures. For example, twoblocks shown in succession may, in fact, be executed substantiallyconcurrently or in parallel, or the blocks may sometimes be executed inthe reverse order, depending upon the functionality involved.Additionally, two blocks shown in parallel may, in fact, be executedsequentially, depending on the functionality involved. It will also benoted that each block of the block diagrams and/or flowchartillustration, and combinations of blocks in the block diagrams and/orflowchart illustration, can be implemented by special purposehardware-based systems that perform the specified functions or acts, orcombinations of special purpose hardware and computer instructions.

Embodiments of the invention are described with reference to flowchartillustrations and/or block diagrams of methods, apparatus (systems) andcomputer program products according to embodiments of the invention. Itwill be understood that a block of the flowchart illustrations and/orblock diagrams, or combinations of blocks in the flowchart illustrationsand/or block diagrams, can be implemented by computer programinstructions. These computer program instructions may be provided to aprocessor of a general purpose computer, special purpose computer, orother programmable data processing apparatus to produce a machine, suchthat the instructions, which execute via the processor of the computeror other programmable data processing apparatus, create means forimplementing the functions/acts specified in the flowchart and/or blockdiagram block or blocks.

These computer program instructions may also be stored in acomputer-readable memory that can direct a computer or otherprogrammable data processing apparatus to function in a particularmanner, such that the instructions stored in the computer-readablememory produce an article of manufacture including instruction meanswhich implement the function/act specified in the flowchart and/or blockdiagram block or blocks.

Any suitable computer usable or computer readable medium may beutilized. The computer-usable or computer-readable medium may be, forexample but not limited to, an electronic, magnetic, optical,electromagnetic, infrared, or semiconductor system, apparatus, device,or propagation medium. More specific examples (a non-exhaustive list) ofthe computer-readable medium would include the following: an electricalconnection having one or more wires, a portable computer diskette, ahard disk, a random access memory (RAM), a read-only memory (ROM), anerasable programmable read-only memory (EPROM or Flash memory), anoptical fiber, a portable compact disc read-only memory (CD-ROM), anoptical storage device, a transmission media such as those supportingthe Internet or an intranet, or a magnetic storage device. Note that thecomputer-usable or computer-readable medium could even be paper oranother suitable medium upon which the program is printed, as theprogram can be electronically captured, via, for instance, opticalscanning of the paper or other medium, then compiled, interpreted, orotherwise processed in a suitable manner, if necessary, and then storedin a computer memory. In the context of this document, a computer-usableor computer-readable medium may be any medium that can contain, store,communicate, propagate, or transport the program for use by or inconnection with the instruction execution system, apparatus, or device.The computer-usable medium may include a propagated data signal with thecomputer-usable program code embodied therewith, either in baseband oras part of a carrier wave. The computer usable program code may betransmitted using any appropriate medium, including but not limited tothe Internet, wireline, optical fiber cable, RF, etc.

Computer program code for carrying out operations of embodiments of theinvention may be written in an object oriented programming language suchas EMCA script, Smalltalk, C++ or the like. However, the computerprogram code for carrying out operations of embodiments of the inventionmay also be written in conventional procedural programming languages,such as C or similar programming languages. The program code may executeentirely on the user's computer, partly on the user's computer, as astand-alone software package, partly on the user's computer and partlyon a remote computer or entirely on the remote computer or server. Inthe latter scenario, the remote computer may be connected to the user'scomputer through a local area network (LAN) or a wide area network(WAN), or the connection may be made to an external computer (forexample, through the Internet using an Internet Service Provider).

The computer program instructions may also be loaded onto a computer orother programmable data processing apparatus to cause a series ofoperational steps to be performed on the computer or other programmableapparatus to produce a computer implemented process such that theinstructions which execute on the computer or other programmableapparatus provide steps for implementing the functions/acts specified inthe flowchart and/or block diagram block or blocks.

The corresponding structures, materials, acts, and equivalents of allmeans or step plus function elements in the claims below are intended toinclude any structure, material, or act for performing the function incombination with other claimed elements as specifically claimed.

Although embodiments of the invention are described with particularapplication to track-following servomechanisms, it should be appreciatedby one of ordinary skill in the art that embodiments of the inventionmay also be applied more generally in digital control systems where asensor that provides a feedback signal introduces a variable delay thatdepends on an observable system parameter.

Having thus described the invention of the present application in detailand by reference to embodiments thereof, it will be apparent thatmodifications and variations are possible without departing from thescope of the invention defined in the appended claims.

1. A track-following servomechanism for a tape drive system, theservomechanism comprising: an actuator coupled to a head module housingat least one servo reader, the actuator configured to actuate motion ofthe head module based on a control signal u(t); a servo channel coupledto the servo reader, the servo channel configured to receive from theservo reader a servo signal s(t) and configured to determine, based onthe servo signal s(t), a lateral position estimate signal y(t)representing a lateral position estimate of the servo reader and a tapevelocity estimate signal v(t) representing longitudinal velocity of atape, wherein the servo channel introduces a tape velocity-dependentdelay τ(v) into the lateral position estimate signal y(t); a predictorfilter coupled to the servo channel, the predictor filter configured toreceive from the servo channel the lateral position estimate signal y(t)and the tape velocity estimate signal v(t), wherein the predictor filterdetermines a modified lateral position estimate signal ŷ(t) that reducesa difference, introduced by the tape velocity-dependent delay τ(v),between the modified lateral position estimate signal ŷ(t) and an actuallateral position; and a compensator coupled to the predictor filter andthe actuator, the compensator configured to output the control signalu(t), wherein u(t) is based upon the modified lateral position estimatesignal ŷ(t).
 2. The servomechanism of claim 1, further comprising: abypass route coupling the servo channel to the compensator, the bypassroute bypassing the predictor filter; and a switch coupled to the servochannel, the bypass route, and the predictor filter, wherein the switchis configured to transmit the lateral position estimate signal y(t)along the bypass route when the tape velocity estimate signal v(t)indicates the velocity of the tape is at or above a threshold velocityand configured to transmit the lateral position estimate signal y(t) tothe predictor filter when the tape velocity estimate signal v(t)indicates the velocity of the tape is below the threshold velocity. 3.The servomechanism of claim 2, wherein the threshold velocity is 1.6m/s.
 4. The servomechanism of claim 1, wherein the predictor filter is aKalman filter.
 5. A track-following servomechanism for a tape drivesystem, the servomechanism comprising: a digital-to-analog converter(DAC) configured to receive a digital control signal u_(d)(t), convertthe digital control signal u_(d)(t) to an analog control signalu_(a)(t), and output the analog control signal u_(a)(t); an actuatorcoupled to the DAC and coupled to a head module housing at least oneservo reader, the actuator configured to receive from the DAC the analogcontrol signal u_(a)(t) and to actuate motion of the head module basedon the analog control signal u_(a)(t); a servo channel coupled to theservo reader, the servo channel configured to receive from the servoreader a servo signal s(t), and the servo channel configured to output alateral position estimate signal y(t) representing a lateral positionestimate of the servo reader and a tape velocity estimate signal v(t)representing longitudinal velocity of a tape; a Kalman filter coupled tothe servo channel, the Kalman filter configured to receive from theservo channel the lateral position estimate signal y(t) and the tapevelocity estimate signal v(t), and to receive the digital control signalu_(d)(t), and the Kalman filter configured to output an estimate of anaugmented actuator state signal {circumflex over (x)}_(aug) (t), and amodified lateral position estimate signal ŷ(t); a controller coupled tothe servo channel and the Kalman filter, the controller configured toreceive from the servo channel the tape velocity estimate signal v(t)and receive from the Kalman filter the estimate of the augmentedactuator state signal {circumflex over (x)}_(aug) (t), and thecontroller configured to output an augmented control signal u_(aug)(t);a subtractor coupled to the Kalman filter, the subtractor configured toreceive from the Kalman filter the modified lateral position estimatesignal ŷ(t), and the subtractor configured to output a differencebetween a reference signal r(t) and the modified lateral positionestimate signal ŷ(t) as a modified error signal ê(t); a compensatorcoupled to the subtractor, the compensator configured to receive fromthe subtractor the modified error signal ê(t), and the compensatorconfigured to output a preliminary digital control signal t_(d0)(t); andan adder coupled to the compensator, the controller, the DAC, and theKalman filter, the adder configured to receive from the compensator thepreliminary digital control signal u_(d0)(t) and from the controller theaugmented control signal u_(aug)(t), and the adder configured to outputto the DAC and to the Kalman filter the digital control signal u_(d)(t).6. The servomechanism of claim 5, wherein the servo channel introduces atape velocity-dependent delay τ(v) into the lateral position estimatesignal y(t), and wherein the servo channel is equivalent to afirst-order low-pass filter having a variable time constant that variesbased on the delay τ(v).
 7. The servomechanism of claim 5, wherein theKalman filter is further configured to determine the estimate of theaugmented actuator state signal {circumflex over (x)}_(aug) (t) and themodified lateral position estimate signal ŷ(t) at discrete timeinstants, wherein t is equal an integer k times a sampling interval T ofthe DAC.
 8. The servomechanism of claim 7, wherein the Kalman filter isconfigured to determine the estimate of the augmented actuator statesignal {circumflex over (x)}_(aug) (t) using:{circumflex over (x)} _(aug,k) = x _(aug,k) +L(y(t _(k))−H x _(aug,k)),andx _(aug,k+1) =F x _(aug,k) +Gu _(k), wherein y(t_(k)) is the lateralposition estimate signal from the servo channel at the discrete timeinstants, L is a 3×1 matrix that represents an innovation gain of theKalman filter, F is a 3×3 matrix, G is a 3×1 matrix, and H is a 1×3matrix, and wherein the matrices F, G, and H give a discrete-timestate-space representation of the servomechanism.
 9. The servomechanismof claim 5, wherein the longitudinal velocity of the tape is 0.6 m/s-1.6m/s.
 10. A method for operating a servomechanism in a tape drive system,the method comprising: receiving a servo signal s(t) from a servoreader; based on the servo signal s(t), determining a lateral positionestimate y(t) of the servo reader; based on the servo signal s(t),determining a velocity estimate v(t) of a tape being read by the servoreader; identifying a tape velocity based on the velocity estimate v(t);if the tape velocity is above a threshold velocity, feeding back thelateral position estimate y(t) to a compensator; if the tape velocity isbelow the threshold velocity, wherein the threshold velocity is avelocity at which a non-negligible tape velocity-dependent delay τ(v) isintroduced into the lateral position estimate signal y(t), transmittingthe lateral position estimate y(t) to a predictor filter, wherein thepredictor filter determines a modified lateral position estimate signalŷ(t) that reduces a difference, introduced by the tapevelocity-dependent delay τ(v), between the modified lateral positionestimate signal ŷ(t) and an actual lateral position, and transmittingthe modified lateral position estimate signal ŷ(t) to the compensator;and outputting from the compensator a control signal for an actuatorcoupled to the servo reader.
 11. The method of claim 10, wherein thethreshold velocity is 1.6 m/s.
 12. The method of claim 10, wherein thepredictor filter is a Kalman filter.
 13. A digital control systemcomprising: a sensor module comprising at least one sensor and anassociated parameter module, wherein the at least one sensor isconfigured to sense an attribute of a physical object, and wherein theassociated parameter module is configured to determine an observablesystem parameter associated with the physical object and affecting theattribute, and wherein the sensor module is configured to provide afeedback signal based on the attribute and a signal representing theobservable system parameter, and wherein the sensor module is tointroduce in the feedback signal a delay dependent on the observablesystem parameter; a predictor filter coupled to the sensor module, thepredictor filter configured to receive from the sensor module thefeedback signal and the signal representing the observable systemparameter, wherein the predictor filter is further configured todetermine a modified feedback signal that reduces a difference,introduced by the delay dependent on the observable system parameter,between the modified feedback signal and an actual physical attribute;and a compensator coupled to the predictor filter, the compensatorconfigured to output a control signal u(t) that is based upon themodified feedback signal, wherein motion of said at least one sensor isbased on the control signal u(t).
 14. The system of claim 13, whereinthe predictor filter is a Kalman filter.
 15. The system of claim 13,wherein the attribute of the physical object is a position of thephysical object and the observable system parameter associated with thephysical object is a velocity of the physical object.